The Liebau mechanism, inspired by embryonic heart function, generates net directional flow through periodic, asymmetric compression of a compliant tube - without the need for valves. This work presents the first free-swimming robot powered solely by Liebau pumping, using an off-center solenoid to create traveling pressure waves that produce bidirectional thrust. The goals of this paper are to map propulsion behavior across key actuation parameters to understand thrust direction and magnitude, optimize tube mechanics to enhance momentum transfer and design efficient, and design, fabricate, and test a concentrically actuating Liebau Pump